# Energy Dissipation Enhanced by Multiple Hinges in Bridge Piers with CFST Y-Shaped Fuses

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Models and Methods

#### 2.1. CFST-Y Bridge Pier Models

_{2}) and the limb height (h

_{1}) varying from 1 m to 7 m individually. The center-to-center spacings (d) between two limb tops range from 1.2 m to 7.2 m. All CFST members are made of Q345 steel tubes with a thickness of 16 mm forming a Y-shaped pier filled with C35 concrete [28]. The bottom end of the column is assumed to be rigidly connected to the foundation cap fixed at ground level and the soil–structure interaction is neglected for simplicity.

#### 2.2. Pushover Methodology

_{a}) with spectral displacement (S

_{d}) [19,33].

#### 2.3. Numerical Models

_{s}) of Q345 steel in the first linear stage, and 0.01 E

_{s}in the post-yielding stage. The confined concrete is divided into 48 fibers described by the Kent–Park model [37,38], which performs well in modeling both the concentrated and the distributed plastic hinges in CFSTs [6].

_{b}at 4370 kN/m, serve as elastic links to support the deck. Two equivalent tributary masses for the pier systems are considered in this work, depending on the corresponding span length and deck material.

## 3. Results and Discussion

#### 3.1. Lateral Stiffnesses for Three Types of Y-Shaped Piers

_{1}and top spacing d) and one vertical pier column (with height h

_{2}). In the two connected limbs, the equivalent moment of inertia of each limb is I

_{1}and the inclined angle between the two limbs is 2α. The lower column, with the equivalent moment of inertia at I

_{2}, connects the two upper limbs rigidly with a casting wye joint.

_{bs}is the shear stiffness of a single bearing, and the lateral stiffnesses of the left and right limbs can be calculated by Equations (4) and (5), respectively.

_{1}, h

_{2}, and d) and the material properties, like E, I

_{1}, and I

_{2}. It indicates that piers with different pier–deck connections have distinct equations of lateral stiffnesses.

_{1}= 0.6 m, d

_{2}= 1.0 m) but with different structural dimensions (h

_{1}, h

_{2}, and d). The lateral stiffnesses (k

_{p}

_{1}, k

_{p}

_{2}, and k

_{p}

_{3}) of the monolithic, the braced articulated and the free articulated piers are calculated and listed in Table 1, respectively. For each case with identical structural dimensions, k

_{p}

_{1}is generally larger than k

_{p}

_{2}and k

_{p}

_{3}. As h increases from 4 m to 10 m with the increase of either h

_{1}or h

_{2}individually, all lateral stiffnesses (k

_{p}

_{1}, k

_{p}

_{2}, and k

_{p}

_{3}) decrease monotonically. The stiffness reduction as a function of h is much more significant for k

_{p}

_{1}than for k

_{p}

_{2}and k

_{p}

_{3}, indicating that the monolithic piers are more sensitive to pier height. The stiffness reduction due to the increase of h

_{1}is larger than that due to h

_{2}. It is noted that the influence of inter-limb spacing d on the lateral stiffnesses of the monolithic piers is not so significant as that of h

_{1}and h

_{2}.

#### 3.2. Ductility Capacities for Piers with Different Pier–Deck Connections

_{u}, defined by the difference between the ultimate deck displacement, u

_{u}, to the corresponding displacement, u

_{y}, at its second yielding.

_{0}, of each pier is determined by the difference between the displacement demand at a given earthquake level and the corresponding displacement at the second yielding.

_{u}

_{1}, Δ

_{u}

_{2}, and Δ

_{u}

_{3}) of the three types of piers, as listed in Table 1, are calculated with Equation (7) based on u

_{u}and u

_{y}obtained from their corresponding capacity spectra. For cases listed in Table 1, the ductility capacity and the corresponding ductility demands at three earthquake levels (SLE, DBE, and MCE) are compared by bar charts, as illustrated in Figure 5. Generally, Δ

_{u}

_{1}, Δ

_{u}

_{2}, and Δ

_{u}

_{3}are comparable to each other with the fixed structural dimensions. For each case with h increasing from 4 m to 10 m, all ductility capacities (Δ

_{u}

_{1}, Δ

_{u}

_{2}, and Δ

_{u}

_{3}) increase monotonically with the increase of either h

_{1}or h

_{2}individually. Yet, as d increases from 1.2 m to 7.2 m, ductility capacities for three types of piers (h

_{1}= h

_{2}= 3 m) do not change significantly, as shown in Figure 5c,f,i. This implies that the pier height, comprising h

_{1}and h

_{2}, is the primary parameter that influences structural ductility.

_{0}less than −0.25 u

_{y}at the first yielding, elastic-plastically with a negative Δ

_{0}larger than −0.25 u

_{y}, and plastically with positive Δ

_{0}. Under the SLE loading, the ductility demand for each case is less than −0.25 u

_{y}. This means that all piers remain elastic upon the SLE demands being reached and the requirement on the immediate occupancy (IO) performance level being achieved. Similar IO performances can be achieved in both the monolithic piers and the braced articulated piers under the DBE loading. Yet, for the free articulated piers, the ductility demands (Δ

_{0}) exceed the corresponding −0.25 u

_{y}and even become positive for piers with heights of 6 m and 8 m. This means that the free articulated piers will deform inelastically to meet the DBE demands that should be checked against the requirements of the life safety (LS) performance. For all considered piers, the ductility demands (Δ

_{0}) at the MCE level are positive, meaning that all piers yield with the formation of plastic hinges to achieve the collapse prevention (CP) performance.

#### 3.3. Ductility Capacities and Lateral Resistances for Piers with Different Structural Dimensions

_{1}or h

_{2}, the lateral resistance decreases, while the ductility capacity increases. In each figure, capacity spectrum curves intersect with their inelastic MCE response spectra at the MCE performance points, denoted as solid circles.

_{l}

_{1}or k

_{l}

_{2}) is rather small relative to the shear keys and column. Under lateral loading, the horizontal displacement at the pier top is distributed according to the slenderness of the structural members. The limb inclined towards the displacement direction is usually the slenderest member and will yield earlier; but at increased h, the slenderer pier can accommodate more deformation and will yield later. This indicates that, besides the pier–deck connection, the yielding behaviors are affected by the distribution of lateral stiffnesses among the bearings and the structural members.

#### 3.4. Ductility Demands at Different Deck Masses, Shear Limits, and Stiffnesses of Bearings

_{1}= h

_{2}= 3 m, d = 3.6 m). Two practical equivalent deck masses (1.0 × 10

^{5}kg and 1.5 × 10

^{5}kg) are considered to study the lateral resistance and the ductility of the interested piers. With either deck mass, the lateral resistance of the monolithic pier is larger than that of the braced articulated pier, and further, the free articulated one; whereas the ductility capacity for the three types of piers is in the opposite order.

_{1}= h

_{2}= 3 m, d = 3.6 m), the ADRS curves for the pushover analyses in the braced and free articulated piers with bearings at different stiffnesses and shear limits are shown in Figure 10 and Figure 11, respectively. Three stiffnesses (0.5k

_{b}, k

_{b}, and 2k

_{b}) and two shear limits (5 cm and 10 cm) are considered for each type of articulated piers.

_{b}to 0.5k

_{b}, as typically shown in Figure 10. For braced articulated piers, both the first and the second yielding points are located between the DBE and MCE performance points; while for each free articulated pier, both yielding points are between the SLE and DBE performance points. This indicates that both articulated piers deform elastically to satisfy their corresponding SLE performance demands, but the free articulated piers will form plastic hinges before the DBE performance demands. Particularly, for the free articulated piers with 0.5k

_{b}, as shown in Figure 11b, a transition occurs before the DBE demand. The early yielding confirms the illustrations in Figure 5g–©, where limbs yield before columns.

#### 3.5. Energy Dissipation before and after the Expected Performance

_{1}and h

_{2}), both ranging from 1 m to 7 m. Consistent with the case (h

_{1}= h

_{2}= 3 m) shown in Figure 12, the energy dissipations of each type of pier differ remarkably before and after the MCE performance and are determined by the structural dimensions. That is, with the identical cross-sections in the CFST-Y piers, the structural dimensions determine the stiffness of structural members and thereby, the absorbed and residual energies.

_{1}, h

_{2}, and d on the horizontal load and displacement can be studied individually based on Figure 14a–c, respectively. With the increase of either h

_{1}or h

_{2}, the ultimate strength of the skeleton curves decreases, while the ultimate displacement increase. This means that the less ultimate strength, always accompanied by the larger ultimate displacement, is determined by h. It is also noted that both the lateral resistance and the ductility capacity are nearly insensitive to d. This confirms that the nonsymmetrical moment near the wye approach joint is insensitive to d and solely determined by the combined stiffnesses (k

_{e}

_{1}or k

_{e}

_{2}) of limb-bearing systems. Here, at the fixed shear limit of 5 cm, the structural ductility of the free articulated pier is primarily determined by the combination of h

_{1}and h

_{2}. Thus, by rationally designing the structural dimensions (h

_{1}and h

_{2}), the local ductility of inclined members can be exploited to dissipate more energy effectively.

## 4. Conclusions

- (1)
- The pier–deck connection and structural dimensions (h
_{1}, h_{2}, and d) determine the lateral stiffnesses and yielding behaviors of the CFST Y-shaped piers that will further influence the lateral resistances and ductility capacities in bridges at the SLE, DBE, and MCE hazard levels. - (2)
- On achieving the expected performance objectives, the ductility demands for all three types of piers increase with the deck mass. Particularly, for the braced and free articulated piers, the ductility demands increase with the shear limit but decrease with the shear stiffness of bearings.
- (3)
- The absorbed and residual energies before and after the expected performance can be utilized to evaluate the ductility exploitation and performance redundancy in CFST-Y piers. The enhanced absorbed energies before the MCE performance were observed in the free articulated piers where the extra energies were dissipated by multiple hinges formed in CFST Y-shaped fuses.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

CFST | concrete-filled steel tubular | |

RC | reinforced concrete | |

CFST-Y | CFST Y-shaped | |

SDF | single-degree-of-freedom | |

S_{a} | spectral acceleration | |

S_{d} | spectral displacement | |

ADRS | Acceleration Displacement Response Spectrum | |

SLE | Service Level Earthquake | |

DBE | Design Based Earthquake | |

MCE | Maximum Credible Earthquake | |

IO | Immediate Occupancy | |

LS | Life Safety | |

CP | Collapse Prevention | |

h | total pier height | |

h_{1} | limb height | |

h_{2} | column height | |

d | center-to-center spacing between the limb tops | |

E_{s} | elastic modulus of Q345 steel | |

α | inclined angle between one limb and the vertical line | |

I_{1} | moment of inertia of limb | |

I_{2} | moment of inertia of column | |

P | equivalent lateral static loading | |

m | effective mass of bridge deck | |

k_{p}_{1} | lateral stiffness of the monolithic piers | |

k_{p}_{2} | lateral stiffness of the braced articulated piers | |

k_{p}_{3} | lateral stiffness of the free articulated piers | |

k_{c}_{1} | lateral stiffness of the upper portion of the Y-shaped pier | |

k_{c}_{2} | lateral stiffness of the lower portion of the Y-shaped pier | |

E | equivalent elastic modulus of CFSTs | |

k_{b} | shear stiffness of bearings in a pier system | |

k_{bs} | shear stiffness of a single bearing | |

k_{l}_{1} | lateral stiffness of the left limb | |

k_{l}_{2} | lateral stiffness of the right limb | |

λ | ratio of the lateral seismic force to the equivalent gravity of deck | |

k_{e}_{1} | equivalent lateral stiffness of the left limb-bearing systems | |

k_{e}_{2} | equivalent lateral stiffness of the left limb-bearing systems | |

Δ_{u} | post-yielding displacement capacity | |

Δ_{0} | ductility demand | |

u_{u} | ultimate deck displacement | |

u_{y} | the second yielding displacement | |

u_{0} | displacement demand at a given earthquake level | |

Δ_{u}_{1} | ductility capacity of the monolithic pier | |

Δ_{u}_{2} | ductility capacity of the braced articulated pier | |

Δ_{u}_{3} | ductility capacity of the free articulated pier |

## References

- Yang, S.; Huang, D. Aesthetic considerations for urban pedestrian bridge design. J. Archit. Eng.
**1997**, 3, 3–8. [Google Scholar] [CrossRef] - Priestley, M. Performance based seismic design. Bull. N. Z. Soc. Earthq.
**2000**, 33, 325–346. [Google Scholar] [CrossRef] [Green Version] - Priestley, M.J.N.; Calvi, G.M.; Kowalsky, M.J. Direct displacement-based seismic design of structures. In Proceedings of the NZSEE Conference, Wellington, New Zealand, 30 March–1 April 2007; pp. 1–23. [Google Scholar]
- D’Amato, M.; Braga, F.; Gigliotti, R.; Kunnath, S.; Laterza, M. A numerical general-purpose confinement model for non-linear analysis of R/C members. Comput. Struct.
**2012**, 102–103, 64–75. [Google Scholar] [CrossRef] - Guney, O.; Saatcioglu, M. Confinement of concrete columns for seismic loading. Struct. J.
**1987**, 84, 308–315. [Google Scholar] - Stephens, M.T.; Lehman, D.E.; Roeder, C.W. Seismic performance modeling of concrete-filled steel tube bridges: Tools and case study. Eng. Struct.
**2018**, 165, 88–105. [Google Scholar] [CrossRef] - Chacon, R.; Mirambell, E.; Real, E. Strength and ductility of concrete-filled tubular piers of integral bridges. Eng. Struct.
**2013**, 46, 234–246. [Google Scholar] [CrossRef] - Elremaily, A.; Azizinamini, A. Behavior and strength of circular concrete-filled tube columns. J. Constr. Steel. Res.
**2002**, 58, 1567–1591. [Google Scholar] [CrossRef] - Marson, J.; Bruneau, M. Cyclic testing of concrete-filled circular steel bridge piers having encased fixed-based detail. J. Bridge Eng.
**2004**, 9, 14–23. [Google Scholar] [CrossRef] - Han, L.-H.; Li, W.; Bjorhovde, R. Developments and advanced applications of concrete-filled steel tubular (CFST) structures: Members. J. Constr. Steel. Res.
**2014**, 100, 211–228. [Google Scholar] [CrossRef] - Roeder, C.W.; Stephens, M.T.; Lehman, D.E. Concrete filled steel tubes for bridge pier and foundation construction. Int. J. Steel Struct.
**2018**, 18, 39–49. [Google Scholar] [CrossRef] - Wang, J.; Kunnath, S.; He, J.; Xiao, Y. Post-Earthquake Fire Resistance of Circular Concrete Filled Steel Tubular Columns. J. Struct. Eng.
**2020**, 146, 1–13. [Google Scholar] [CrossRef] - Chung, Y.-S.; Park, C.K.; Meyer, C. Residual seismic performance of reinforced concrete bridge piers after moderate earthquakes. ACI. Struct. J.
**2008**, 105, 87–95. [Google Scholar] - Bertero, R.D.; Bertero, V.V. Redundancy in earthquake-resistant design. J. Struct. Eng.
**1999**, 125, 81–88. [Google Scholar] [CrossRef] - Paulay, T.; Priestley, M. Seismic Design of Reinforced Concrete and Masonry Buildings; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 1992; pp. 95–157. [Google Scholar]
- Bovo, M.; Savoia, M.; Praticò, L. Seismic Performance Assessment of a Multistorey Building Designed with an Alternative Capacity Design Approach. Adv. Civ. Eng.
**2021**, 2021, 5178065. [Google Scholar] [CrossRef] - Zhang, C.; Tian, Y. Simplified performance-based optimal seismic design of reinforced concrete frame buildings. Eng. Struct.
**2019**, 185, 15–25. [Google Scholar] [CrossRef] - Kia, S.M.; Yahyai, M. Relationship between local and global ductility demand in steel moment resisting frames. In Proceedings of the World Conference on Earthquake Engineering WCEE, Vancouver, BC, Canada, 1–6 August 2004. [Google Scholar]
- Fajfar, P. Capacity spectrum method based on inelastic demand spectra. Earthq. Eng. Struct. D
**1999**, 28, 979–993. [Google Scholar] [CrossRef] - Yang, T.Y.; Tung, D.P.; Li, Y. Equivalent energy design procedure for earthquake resilient fused structures. Earthq. Spectra.
**2018**, 34, 795–815. [Google Scholar] [CrossRef] - Zou, X.K.; Chan, C.M. Optimal seismic performance-based design of reinforced concret-e buildings using nonlinear pushover analysis. Eng. Struct.
**2005**, 27, 1289–1302. [Google Scholar] [CrossRef] - Ghobarah, A. Performance-based design in earthquake engineering: State of development. Eng. Struct.
**2001**, 23, 878–884. [Google Scholar] [CrossRef] - Cardone, D.; Dolce, M.; Palermo, G. Direct displacement-based design of seismically isolated bridges. Bull. Earthq. Eng.
**2009**, 7, 391–410. [Google Scholar] [CrossRef] - Guo, W.; Hu, Y.; Liu, H.; Bu, D. Seismic performance evaluation of typical piers of China’s high-speed railway bridge line using pushover analysis. Math. Probl. Eng.
**2019**, 2019, 95147691. [Google Scholar] [CrossRef] - Wang, P.-H.; Chang, K.-C.; Dzeng, D.-C.; Lin, T.-K.; Hung, H.-H.; Cheng, W.-C. Seismic evaluation of reinforced concrete bridges using capacity-based inelastic displacement spectra. Earthq. Eng. Struct. Dyn.
**2021**, 50, 1845–1863. [Google Scholar] [CrossRef] - Sadeghi, M.A.; Yang, T.Y.; Bagatini-Cachuço, F.; Pan, S. Seismic design and performance evaluation of controlled rocking dual-fused bridge system. Eng. Struct.
**2020**, 212, 110467. [Google Scholar] [CrossRef] - Liu, Q.F.; Zhu, S.M.; Yu, W.S.; Wu, X.; Song, F.; Ren, X. Ground Motion Frequency Insensit-ivity of Bearing Supported Pedestrian Bridge with Viscous Dampers. KSCE. J. Civ. Eng.
**2021**, 25, 2662–2673. [Google Scholar] [CrossRef] - JTG/T 2231-01-2020; Specifications for Seismic Design of Highway Bridges. Chongqing Communications Research Institute: Chongqing, China; People’s Communication Publishing: Beijing, China, 2020.
- FEMA. NEHRP Guidelines for the Seismic Rehabilitation of Buildings; FEMA-273; Applied Technology Council for the Building Seismic Safety Council: Washington, DC, USA, 1997. [Google Scholar]
- Krawinkler, H.; Seneviratna, G. Pros and cons of a pushover analysis of seismic performance evaluation. Eng. Struct.
**1998**, 20, 452–464. [Google Scholar] [CrossRef] - Calvi, G.M.; Pavese, A. Conceptual design of isolation systems for bridge structures. J. Earthq. Eng.
**1997**, 1, 193–218. [Google Scholar] [CrossRef] - ATC-40; Seismic Evaluation and Retrofit of Concrete Buildings. Applied Technology Council: Redwood City, CA, USA, 1996.
- Fajfar, P. A nonlinear analysis method for performance-based seismic design. Earthq. Spectra.
**2000**, 16, 573–592. [Google Scholar] [CrossRef] - Lagaros, N.D.; Fragiadakis, M. Evaluation of ASCE-41, ATC-40 and N
_{2}static pushover methods based on optimally designed buildings. Soil. Dyn. Earthq. Eng.**2011**, 31, 77–90. [Google Scholar] [CrossRef] - McKenna, F. Open System for Earthquake Engineering Simulation. OpenSees. Available online: https://opensees.berkeley.edu/ (accessed on 3 July 2020).
- Midas/Civil. Nonlinear FE Software for Bridge Design & Analysis; Midas Information Technology Co., Ltd.: Seongnam, Korea, 2000. [Google Scholar]
- Scott, B.D.; Park, R.; Priestley, M.J.N. Stress-Strain Behavior of Concrete Confined by Overlapping Hoops at Low and High Strain Rates. J. Proc.
**1982**, 79, 13–27. [Google Scholar] - Susantha, K.; Ge, H.; Usami, T. Uniaxial stress-strain relationship of concrete confined by various shaped steel tubes. Eng. Struct.
**2001**, 23, 1331–1347. [Google Scholar] [CrossRef] - JTJ 663-2006; Series of Elastomeric Pad Bearings for Highway Bridges. CCCC Highway Consultants Co., Ltd. People’s Communications Publishing: Beijing, China, 2007.
- GB50011-2010; Code for Seismic Design of Buildings. China Ministry of Construction. China Architecture & Building Press: Beijing, China, 2010.
- Fan, L.C.; Zhuo, W.D. Ductility Seismic Design of Bridges; People’s Communication Publishing: Beijing, China, 2001. [Google Scholar]
- Sigurdardottir, D.H.; Glisic, B. Measures of Structural Art: A Case Study Using Streicker Bridge; Princeton University: Princeton, NJ, USA, 2013; pp. 275–284. [Google Scholar]
- Abey, E.T.; Somasundaran, T.P.; Sajith, A.S. Significance of elastomeric bearing on seismic response reduction in bridges. In Advances in Structural Engineering; Springer: New Delhi, India, 2015; pp. 1339–1352. [Google Scholar]

**Figure 1.**Sketches and typical pier models for three types of bridges with the monolithic piers (

**a**), the braced articulated piers (

**b**), and the free articulated piers (

**c**), respectively.

**Figure 3.**SDF finite element models for the braced articulated pier systems with a typical fibred column cross-section.

**Figure 4.**Simplified diagrams for CFST-Y pier systems with the monolithic (

**a**) and the articulated pier–deck connections with (

**b**) or without bracing (

**c**).

**Figure 5.**Ductility demands, ductility capacities, and yielding behaviors for piers with the monolithic connection (

**a**–

**c**), the articulated connections with (

**d**–

**f**) and without bracing (

**g**–

**i**) at varying structural dimensions.

**Figure 7.**ADSRs for the braced articulated piers at different limb heights (

**a**) and column heights (

**b**).

**Figure 8.**ADSRs for the free articulated piers at different limb heights (

**a**) and column heights (

**b**).

**Figure 10.**ADRSs for pushover analyses in braced articulated piers with bearing shear limits of 5 cm (

**a**) and 10 cm (

**b**).

**Figure 11.**ADRSs for pushover analyses in free articulated piers with bearing shear limits of 5 cm (

**a**) and 10 cm (

**b**).

**Figure 12.**Hysteretic curves for the monolithic (

**a**), the braced articulated (

**b**), and the free articulated (

**c**) CFST-Y piers with h

_{1}= h

_{2}= 3 m and d = 3.6 m.

**Figure 13.**Contour diagrams of the absorbed energy (upper) and the residual energy (bottom) in achieving the MCE performance for the monolithic (

**a**), the braced articulated (

**b**), and the free articulated piers (

**c**) with different structural dimensions.

**Figure 14.**Skeleton curves in the free articulated piers at different h

_{1}(

**a**), h

_{2}(

**b**), and d (

**c**).

**Table 1.**Lateral stiffnesses and ductility capacities for three groups of piers with varying structural dimensions.

h (m) | h_{1}(m) | h_{2}(m) | d (m) | k_{p}_{1} (10^{3} kN/m) | Δ_{u}_{1} (cm) | k_{p}_{2} (10^{3} kN/m) | Δ_{u}_{2} (cm) | k_{p}_{3} (10^{3} kN/m) | Δ_{u}_{3} (cm) |
---|---|---|---|---|---|---|---|---|---|

4 | 1 | 3 | 3.6 | 93.09 | 9.01 | 7.97 | 8.15 | 7.71 | 8.41 |

6 | 3 | 3 | 3.6 | 20.83 | 15.01 | 6.91 | 14.71 | 5.90 | 14.01 |

8 | 5 | 3 | 3.6 | 7.05 | 29.51 | 4.88 | 29.51 | 4.39 | 27.81 |

10 | 7 | 3 | 3.6 | 3.11 | 31.01 | 3.48 | 30.61 | 2.66 | 30.22 |

4 | 3 | 1 | 3.6 | 39.40 | 6.65 | 8.19 | 6.81 | 6.81 | 6.81 |

6 | 3 | 3 | 3.6 | 20.83 | 15.01 | 6.91 | 14.71 | 5.90 | 14.01 |

8 | 3 | 5 | 3.6 | 10.87 | 19.01 | 5.30 | 19.45 | 4.68 | 18.01 |

10 | 3 | 7 | 3.6 | 6.06 | 24.71 | 3.82 | 24.21 | 3.49 | 23.55 |

6 | 3 | 3 | 1.2 | 21.95 | 14.51 | 6.97 | 14.41 | 6.18 | 13.85 |

6 | 3 | 3 | 3.6 | 20.83 | 15.01 | 6.91 | 14.71 | 5.90 | 14.01 |

6 | 3 | 3 | 6.0 | 19.16 | 15.11 | 6.84 | 15.31 | 4.91 | 15.21 |

6 | 3 | 3 | 7.2 | 18.29 | 16.31 | 6.80 | 15.81 | 4.58 | 15.51 |

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**MDPI and ACS Style**

Liu, Q.; Guo, Z.; Wu, X.; Lu, K.; Ren, X.; Xiao, J.
Energy Dissipation Enhanced by Multiple Hinges in Bridge Piers with CFST Y-Shaped Fuses. *Symmetry* **2022**, *14*, 2371.
https://doi.org/10.3390/sym14112371

**AMA Style**

Liu Q, Guo Z, Wu X, Lu K, Ren X, Xiao J.
Energy Dissipation Enhanced by Multiple Hinges in Bridge Piers with CFST Y-Shaped Fuses. *Symmetry*. 2022; 14(11):2371.
https://doi.org/10.3390/sym14112371

**Chicago/Turabian Style**

Liu, Qunfeng, Zhaoyang Guo, Xing Wu, Kaile Lu, Xiang Ren, and Jialong Xiao.
2022. "Energy Dissipation Enhanced by Multiple Hinges in Bridge Piers with CFST Y-Shaped Fuses" *Symmetry* 14, no. 11: 2371.
https://doi.org/10.3390/sym14112371